Mathematical models are playing an increasing role in the design and manufacture of complex engineered products across a variety of sectors, including automotive and aerospace applications. The aim of the models is to map sets of design choices (e.g. injection timings in a diesel engine; choice of precious metals in an after-treatment system) through to sets of product attributes (e.g. engine efficiency; exhaust emissions). The mapping may involve multi-physics simulations that require significant computational time to run and the outputs are also typically subject to uncertainty. In this setting, manufacturers attempt to identify optimal designs that balance performance across the different attributes and that are also robust to uncertainty.
A major challenge in the design process is the limited budget that is available for the number of candidate solutions that can be examined (due to the hours or days of run-time required to evaluate a solution using a high-fidelity model). Whilst typical optimization algorithms might require tens of thousands of solution iterations to converge on an optimal solution, in this scenario we are restricted to a much smaller budget (normally around 500 trial solutions). The usual practice, therefore, is to first expend part of the budget on estimating a fast emulator/low-fidelity model/surrogate model that can be used to approximate the high-fidelity model. The optimizer is then run on the emulator, with the best identified solutions subsequently re-evaluated using the more computationally expensive high-fidelity model.
There remain various open questions regarding the use of emulation within optimization. This PhD will explore the relationship between emulation and optimization processes and aim to develop novel approaches that combine the two processes into an efficient algorithm framework for optimization on a budget. There will be the opportunity to shape and test the methods within the wider Programme for Simulation Innovation (PSi) funded by EPSRC and Jaguar Land Rover.
This three-year scholarship is funded through the EPSRC Doctoral Training Grant scheme:
• Full award: £14,296 p.a. tax-free stipend + tuition fees – available to UK nationals and EU nationals who have been resident in the UK for at least the last three years. • Fees-only award: tuition fees – available to EU nationals.
A minimum of a Class 2.i honours degree in mathematics / physics / engineering (or related discipline) is required. Good undergraduate coverage of statistics is desirable.
The supervisory team will be Dr Robin Purshouse of the Department of Automatic Control and Systems Engineering and Professor Jeremy Oakley of the School of Mathematics and Statistics.